JDQZ

Matlab® implementation of the JDQZ algorithm. The JDQZ algorithm can be used for computing a few selected eigenvalues with some desirable property together with the associated eigenvectors of a matrix pencil A-lambda*B. The matrices can be real or complex, Hermitian or non-Hermitian, .... The algorithm is effective especially in case A and B are sparse and of large size. The Jacobi-Davidson method is used to compute a partial generalized Schur decomposition of the pair (A,B). The decomposition leads to the wanted eigenpairs.

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References in zbMATH (referenced in 600 articles , 1 standard article )

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  1. Golub, Gene H.; van der Vorst, Henk A.: Eigenvalue computation in the 20th century (2000)
  2. Golub, Gene H.; Zhang, Zhenyue; Zha, Hongyuan: Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations (2000)
  3. Morgan, Ronald B.: Preconditioning eigenvalues and some comparison of solvers (2000)
  4. Morgan, Ronald B.: Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations (2000)
  5. Ruhe, A.: The rational Krylov algorithm for nonlinear matrix eigenvalue problems (2000)
  6. Sameh, Ahmed; Tong, Zhanye: The trace minimization method for the symmetric generalized eigenvalue problem (2000)
  7. Wu, Kesheng; Simon, Horst: Thick-restart Lanczos method for large symmetric eigenvalue problems (2000)
  8. Bai, Zhaojun; Day, David; Ye, Qiang: ABLE: An adaptive block Lanczos method for non-Hermitian eigenvalue problems (1999)
  9. Dohlus, M.; Schuhmann, R.; Weiland, T.: Calculation of frequency domain parameters using 3D eigensolutions (1999)
  10. Elsner, Ulrich; Mehrmann, Volker; Milde, Frank; Römer, Rudolf A.; Schreiber, Michael: The Anderson model of localization: A challenge for modern eigenvalue methods (1999)
  11. Engelborghs, Koen; Roose, Dirk: Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations (1999)
  12. Fattebert, Jean-Luc: Finite difference schemes and block Rayleigh quotient iteration for electronic structure calculations on composite grids (1999)
  13. Fokkema, Diederik R.; Sleijpen, Gerard L. G.; van der Vorst, Henk A.: Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils (1999)
  14. Jia, Zhongxiao: Composite orthogonal projection methods for large matrix eigenproblems (1999)
  15. Jia, Zhongxiao: Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm (1999)
  16. Baglama, J.; Calvetti, D.; Reichel, L.; Ruttan, A.: Computation of a few small eigenvalues of a large matrix with application to liquid crystal modeling (1998)
  17. Edelman, Alan; Arias, Tomás A.; Smith, Steven T.: The geometry of algorithms with orthogonality constraints (1998)
  18. Fokkema, Diederik R.; Sleijpen, Gerard L. G.; Van der Vorst, Henk A.: Accelerated inexact Newton schemes for large systems of nonlinear equations (1998)
  19. Grimme, E.; Gallivan, K. A.; Van Dooren, P. M.: On some recent developments in projection-based model reduction (1998)
  20. Lehoucq, R. B.; Meerbergen, Karl: Using generalized Cayley transformations within an inexact rational Krylov sequence method (1998)

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